Problem: Simplify to lowest terms. $\dfrac{48}{18}$
There are several ways to tackle this problem. What is the greatest common factor (GCD) of 48 and 18? $48 = 2\cdot2\cdot2\cdot2\cdot3$ $18 = 2\cdot3\cdot3$ $\mbox{GCD}(48, 18) = 2\cdot3 = 6$ $\dfrac{48}{18} = \dfrac{8 \cdot 6}{ 3\cdot 6}$ $\hphantom{\dfrac{48}{18}} = \dfrac{8}{3} \cdot \dfrac{6}{6}$ $\hphantom{\dfrac{48}{18}} = \dfrac{8}{3} \cdot 1$ $\hphantom{\dfrac{48}{18}} = \dfrac{8}{3}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{48}{18}= \dfrac{2\cdot24}{2\cdot9}= \dfrac{2\cdot 3\cdot8}{2\cdot 3\cdot3}= \dfrac{8}{3}$